A rigid vessel containing a 3:1 mol ratio of carbon dioxide and water vapor is held at 200 °C where it has a total pressure of 202.7 kPa. If the vessel is cooled to 10 °C so that all of the water vapor condenses, what is the pressure of carbon dioxide? Neglect the volume of the liquid water that forms on cooling.

Video transcript

Hi everyone. The total pressure of an unknown gas in water in a closed container is 708.3. Tour At 150°C. I'm gonna ask to determine the partial pressure Of the unknown gas at the condensing water at 6°C. If the mole ratio was 4 - three. So after condensing water, all the gas pressure is due to the unknown gas. We need to use our partial pressure equation, which is the partial pressure of a gas. It goes to the total pressure has a more fraction of a gas. We have the total pressure. So we need to find a more fraction of the unknown gas. Recall that the mole fraction of a gas because um all of us are you divided by the total number of moles for the more fraction of the unknown gas. It's for moles By about 4-plus 3. Does it have a 43 mole ratio? So the mole fraction of the unknown gas. 0.5714. Now, we can put this into the partial pressure equation, we're gonna get pressure of the unknown gas. It was a total pressure times the mole fraction of the unknown gas. So the pressure pressure of the unknown gas Equals 708.3 Tour Time. The pressure of the unknown gas, It's 404 0.72 toward Now we can find the partial pressure of the unknown gas. After condensing water using gala sacks gas law. Since only the pressure and temperature are changing. We're gonna have p. one over T. One. It was P two over 22. You want? It's 404 .72. Tour. He won Is 150°C. But we need to convert to Kelvin. We're gonna add 273 115 To get 15 Calvin U. two is what we're looking for. And T. Two Is 6°C Plus 273.15 Equals 279 15 kelvin Snappy rearranged the equation and solve for p. two p. 2. It goes p. one T. Two About about T. one. We're Gonna Get P. two. It was 404 0.72 four. I'm 279. 157 About about 423 0.15 Calvin over P. Two. We're gonna get 267 torque. Thanks for watching my video and I hope it was helpful